Question

Which of the following is equal to the rational expression when x -2 or -6?

Answer 1

The given expression is

$f(x) = \frac{3(x+2}{(x+2)(x+6)}$

And since we have x+2 common in numerator and denominator, there is a hole at x+2=0, that is at x=-2

And a function is undefined when denominator is zero. And at x=-6, denominator become zero.

So, at x=-6, the function is undefined, or there is a vertical asymptote at x=-6 and hole at x=-2 .